# Why will two bubbles floating on water surface attract each other?

Two identical bubbles floating on water surface will form clumps, according to the "cheerio effect". But what's the detail about the force? It's necessary to calculate the shape of water surface, in order to find the force?

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An intuitive explanation lies in the idea that (unless I'm mistaken) the attraction results from the fact that the joining of the bubbles results in a reduction in the effective surface area of the system, which minimizes the total surface tension energy. Thinking of the process as a continuous deformation from initial state to final state, the driving force behind the process is this surface energy minimization. As far as finding an explicit closed form for the force, I imagine it might be a bit complicated. – DumpsterDoofus Mar 6 '14 at 17:20
I'm not convinced they "attract" each other. When they bump into each other they tend to join and form a state of lower energy. – SimpleLikeAnEgg Mar 7 '14 at 20:18

They also provide an answer for the force of interaction between two particles with a Radius $R$: $$F(l)=-2 \pi R B^{5/2}\Sigma^2 K_1\left(\frac{l}{L_c}\right)$$
With Bond number $B= \frac{R^2}{L^2_c}$, $L_c=\sqrt{\gamma/\rho g}$, $\Sigma$ a dimensionless Archimedes weight parameter and $K_1$ a first order Bessel function.